High-index UV optical materials may be needed for the next generation immersion lithography to achieve 32-nm image resolution. The image resolution for lithography can be expressed in the following equation:R=K×λ/NA Where R=Image Resolution
K=factor=0.5
λ=wavelength of light source=193 nm
NA=numerical aperture
=nresist sin θresist=nfluid sin θfluid=nlens sin θlens 
nx=index of refraction of respective media x.
Clearly, from the equation, to achieve maximum resolution for photolithography one must increase the numerical aperture (NA) of the optical system, since the K factor and the wavelength of the light source are already fixed. The ideal situation to maximize the aperture is that nlens≧nfluid≧nresist. Since the refractive index of photo-resist is also typically fixed at nresist=1.7, it also sets the lower limit of the refractive indices of the immersion fluid and the optical lens. Typical immersion oil has an index of 1.51. Fluid media with even higher indices (nfluid≧1.65) are being developed. As the refractive index of the immersion fluid increases, the refractive index of the corresponding contact lens also needs to be increased. One would like to have an immersion optical lens with a refraction index greater than 1.7. In “High-index Materials for 193 nm Immersion Lithography”, published in the Proceedings of SPIE Vol. 5754, p. 611-621, Optical Microlithography XVIII (2005), J. H. Burnett, S. G. Kaplan, E. L. Shirley, P. J. Tompkins, and J. E. Webb provided a simple illustration for the desirable condition to use the high index lens and fluid to match with the high index of photoresist to achieve maximum NA. (FIG. 1). A current CaF2 lens with a refractive index of 1.50 at 193 nm will not achieve the desired numerical aperture (NA≧1.5).
When selecting suitable compounds for an optical lens, the crystalline candidate materials should be cubic in crystal symmetry and isotropic in optical properties. This desired property eliminates more than 90% of the known compounds. Among the cubic optical transparent materials, fluoride crystals such as CaF2, SrF2 and BaF2 generally have a high band edge (>8 eV) and high transparency (<140 nm) in the short UV range. Unfortunately, because of the highly ionic nature of the chemical bonding, the refractive indices are generally low. The indices of refraction at 193 nm (20° C.) are 1.50, 1.51 and 1.58, respectively. A recent report from Japan by H. Sato, Y. Inui, I. Masada, T. Nawata, E. Nishijima and T. Fukuda, published in the Print of Proceeding of SPIE—Optical Microlithography XIX, San Jose (2006), showed two new fluoride crystals, KY3F10 and BaLiF3, with refractive indices at 193 nm to be 1.59 and 1.64, respectively. It is an improvement over BaF2 but still much less than desired range of greater or equal to 1.7.
It seems clear that in order to achieve the desired refractive index, it is unlikely that fluoride compounds will be suitable. One may look for a wide band gap material in the oxide compounds. Unfortunately, oxide compounds are, in general, less ionic and the oxygen ion is more polarizable. This means that the band edge will be reduced as compared with fluorides. However, it does gain the increase of refractive indices that are desired in this application. The decrease of the band edge is not desirable. This renders most of the oxide compounds unable to meet the desired band edge property of 7.0 eV or higher. The references “High-index materials for 193 nm and 157 nm immersion lithography”, in International Symposium on Immersion & 157 nm Lithography, Walt Trybula, ed., International SEMATECH, Austin Tex. (2004), by J. H. Burnett, S. G. Kaplan, E. L. Shirley, and J. E. Webb; “High-index Materials for 193 nm Immersion Lithography”, published in the Proceedings of SPIE Vol. 5754, p. 611-621, Optical Microlithography XVIII (2005) by J. H. Burnett, S. G. Kaplan, E. L. Shirley, P. J. Tompkins, and J. E. Webb; and “High-index optical materials for 193-nm immersion lithography”, Print of Proceeding of SPIE—Optical Microlithography XIX, San Jose (2006), by J. H. Burnett, S. G. Kaplan, E. L. Shirley, D. Horowitz, W. Clauss, A. Grenville, and C. Van Peski (collectively referred to as the “Burnett References”) have documented an extensive search of wide band gap oxide compounds. The Burnett References identify only three groups of compounds—simple oxides, aluminates and garnets—that might display the desired band edge property.
For the simple oxides, MgO seems to be the only option having an adequate band edge of 7.6 eV. None of the other alkali earth oxides (CaO, SrO and BaO) nor the rare earth oxides (La2O3, Y2O3, Lu2O3 and Sc2O3) has wide enough band gaps to be desirous. So these simple oxides may be eliminated from further consideration. For aluminates, the Burnett References have identified MgAl2O4 (spinel) and ceramic spinel as the only compounds with adequate band gaps of 7.75 and 7.3 eV, respectively. For the garnets, the Burnett References have identified Lu3Al5O12 (LuAG) as the only aluminum garnet with barely wide enough band edge (≈ 6.9 eV). This is the only garnet capable to produce large size single crystals with known technology. Silicate garnets such as Mg3Al2Si3O12 (pyrope) and Ca3Al2Si3O12 (grossular) do have the adequate band edge near 7.5 eV or more. Unfortunately, silicate garnets can only be grown hydrothermally under high temperature and pressure conditions. For example, pyrope requires tens of kilo-bars of pressure to produce such crystals. So it is unlikely using current known technology to be able to produce a large size of these crystals with the high perfection suitable for this application. Another possibility would be the germinate garnets. So far only Mg3Al2Ge3O12 has the band edge at 6.7 eV. None of the others have enough band edge for consideration. The germinate garnet can only be produced by flux growth. There is serious doubt that the growth technique will ever make sufficiently high quality crystals for UV optical lens applications.
In addition to the UV transparency or band edge test, another consideration for a UV optical element is the intrinsic birefringence (IBR) test. The lens design has a targeted specification of ≦10 nm/cm. MgO has an IBR of ≈70 nm/cm. This is too large a value, thus precluding it from further consideration. MgAl2O4 spinel has one of the highest UV transparencies among the oxide compounds. But its IBR of 52 nm/cm may also be too large to be considered as a suitable UV lens material. Ceramic spinel has the advantage of averaging out the IBR with random orientations of the ceramic grains. However, one drawback is that the ceramic grain structure reduces the light transmittance at 193 nm. Among the garnet materials, LuAG has the highest UV transparency and also the highest index of refraction of 2.14. Moreover, its IBR is 30 nm/cm, which is three times higher than the targeted specification. The reason is due to the very large unit cell with 8 formula units or 160 atoms as compared with 2 atoms per primitive cell for MgO and 14 atoms per primitive cell for MgAl2O4 spinet. Oxygen ions, with the largest polarizability, form cages surrounding the cations. These cages have many orientations that effectively cancel out the IBR, similar to the ceramic situation with randomly oriented microcrystals.
Another consideration for a UV optical element is the transparency at the 193 nm wavelength. It may be preferable that there be at least 90% transmission through the final lens element of approximately 4 cm thick. This requires an absorption coefficient of A10≦0.01 cm−1. Single crystals are well suited to display such a property, if the band gap of the crystal is larger than 6.41 eV (or 193 nm). To ensure the high transmission at 193 nm, one should select a material with a band gap of 7.0 eV and more preferably greater than 7.5 eV (or 160 nm). Ceramic spinel can have a negligible IBR due to the randomly oriented microcrystals and a large enough band gap of 7.3 eV (170 nm). Unfortunately, typical grain sizes of these microcrystals in a ceramic spinel average 50 microns or more. Such grain boundaries create large scattering to attenuate the optical transmission at 193 nm.
In addition to these transmission considerations, the material of a UV optical element should also perform well in the optical uniformity test. Optical crystals can easily have stress-induced birefringence (SBR). The general lithography optics would require an index homogeneity of ≈1 nm/cm. The core defect of LuAG would not be acceptable for an optical lens. For most crystals without such defect induced inhomogeneity, one can remove most of the SBR by a proper thermal annealing process.
Another consideration for a UV optical element is the ability to produce large size single crystals to make the optics. Among the known compounds under evaluation, MgO has too high a melting point to grow a good quality crystal. MgAl2O4 spinel also has high melting temperature (2150° C.) that will limit the maximum size crystal available. LuAG has the capability to produce crystals greater than 100 mm in diameter. However, the facet developed during growth will form a core defect that will greatly reduce the usable size of the material. Other garnets under consideration are not congruent melting so that it is doubtful that any of them can be made into a suitable size with a reasonable time or cost.
The final considerations for a material considered for use as a UV optical element are the physical integrity and chemical stability tests. Ideally, it is preferable that the material has no cleavage plane, good hardness and is chemically inert, so it is relatively easy to make into an immersion lens with good chemical and mechanical durability. All the known oxides under evaluation seem to have good mechanical strength. Any new material developed for such application should also pass most or all of these screening tests.